I couldn't find this in an FAQ here, but I thought I remembered seeing something on the MINIusa site.
At least in the US, automatic traction control (inexplicably All Season traction Control rather than ATC) is standard for the S (hardtop and convertible) (I'm looking at my 2005 spec sheet -- things may have changed in 2006 and almost certainly are different in different countries).
DSC (Dynamic Stability Control) is an option for either Mini Cooper or Mini Cooper S.
DSC includes automatic traction control.
The 2005 owner's manual has nearly identical descriptions, but says ASC works by reducing engine power or apply brakes to the front wheels, while
DSC works by reducing RPMS or applying brakes to individual wheels -- presumably rears as well as front. Both of these can be thought of as anti-lock brakes on steroids. Using the ABS system for traction control is becoming more common even on SUVs since it will work even with open differentials. It does require a more complex ABS system though with individual sensors on each wheel, and individual control of the brakes for each wheel.
You can disable ASC using the toggle switch, just as you would for
DSC. But it's all or nothing -- if you have
DSC you can't switch to an ASC only mode.